When drawing a line is hard

Connecting the dots between math, technology, and law in the challenges of gerrymandering

Miranda Bogen
Sep 14, 2017 · 11 min read
Source: Washington Post

Gerrymandering isn’t just a math problem — it’s a policy fight, legal quagmire, mapping challenge, and statistical puzzle, all wrapped into one

I recently attended Geometry of Redistricting, the first of several workshops of mathematicians, legal advocates, and computer scientists devoted to working through this very conversation, and learned about some of the complexities of the issue firsthand. From the workshop sessions and questions that participants raised, it’s clear that making these interdisciplinary discussions productive and making progress on gerrymandering will require policy professionals to get more than a bit comfortable with math and computers, and vice versa.

What is gerrymandering?

The word “gerrymandering” was coined in 1812, inspired by an oddly-shaped district in South Essex, MA that resembled a salamander. Critics argued that those in power clearly drew the district to benefit their own party in future elections. The practice is still quite common today — so much so, some fear it has reduced electoral competition and amplified ideological polarization.

Adapted from Steven Nass

The many ways to measure gerrymandering

It’s a lot less straightforward to measure gerrymandering than many might think. The experts at the conference were clear that no one-size-fits-all mathematical measure can capture all of the relevant information. But a range of different techniques have been developed, each with their own strengths and imperfections. Here are a few the conference speakers highlighted:

The “efficiency gap”

A simple formula to detect partisan gerrymandering, the efficiency gap metric, was proposed by scholars in 2015. It measures the difference between the number of “wasted” votes in a particular district, by party. Wasted votes include all votes for the losing party, and any votes for the winning party that were not necessary for victory.

Wisconsin’s 2012–2014 districting plan is in red (Simon Jackson)


Compactness is an established redistricting principle that districts should not be highly irregularly shaped.

Source: Washington Post
North Carolina’s 12th district has been flagged as one of the most egregious examples of gerrymandering (Image: NPR)
Adapted from Azavea: Redistricting the Nation
Source: Branden Rishel
Source: Justin Solomon, MIT

A new technique

The Tufts-based research group that put on the conference — the Metric Geometry and Gerrymandering Group — is exploring a new measure based on a geometric characteristic called curvature, which doesn’t use any information about geometric borders. Instead, this method looks at census tracts and graphs them as if they were nodes in a network, connecting the nodes when the tracts are adjacent.

North Carolina’s 12th district, mapped by adjacent census tracts (Source: Moon Duchin)
Adjacency of census units might be difficult to determine in some cases (Source: Justin Solomon)

Why supercomputers can’t solve this for us

Applying the metrics in the previous section, among others, computers can help map drawers and voting advocates compare the relative merits of various districting plans. Alternative maps can provide powerful critiques to dubious districting plans, illustrating the range of possibilities and the tradeoffs — involving compactness, efficiency, minority voting power, district competitiveness, and other factors — that each option would present.

Equal Future

Social justice & technology.

Miranda Bogen

Written by

Senior Policy Analyst at @teamupturn, focused on algorithmic fairness, automation and international tech policy.

Equal Future

Social justice & technology.